Hagen-Poiseuille flow solutions in Grad-type equations (Q633131)

The author considers the Hagen-Poiseuille flow beyond the hydrodynamic regime including boundary conditions which take into account wall properties and non-zero slip velocity using Grad's equations and regularized equations, both in the 13 moment approximation. Analytical results of both approximations are obtained and such results are compared, mainly for the velocity profile and the total volume flow. A set of equations is established for a rarefied gas, where mass, momentum, energy as well as heat flux and the pressure tensor are the relevant variables. The corresponding boundary values for these variables are estimated, where the boundary conditions are based on Maxwell-type conditions which depend on wall properties and on the accommodation coefficient.